Problem: Simplify the following expression: $ r = \dfrac{-8}{5} + \dfrac{-5x}{-6x + 9} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-6x + 9}{-6x + 9}$ $ \dfrac{-8}{5} \times \dfrac{-6x + 9}{-6x + 9} = \dfrac{48x - 72}{-30x + 45} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{-5x}{-6x + 9} \times \dfrac{5}{5} = \dfrac{-25x}{-30x + 45} $ Therefore $ r = \dfrac{48x - 72}{-30x + 45} + \dfrac{-25x}{-30x + 45} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{48x - 72 - 25x}{-30x + 45} $ $r = \dfrac{23x - 72}{-30x + 45}$ Simplify the expression by dividing the numerator and denominator by -1: $r = \dfrac{-23x + 72}{30x - 45}$